example
Solve:
y+9=5.
Solution
|
y+9=5 |
Subtract 9 from each side to undo the addition. |
y+9−−9=5−−9 |
Simplify. |
y=−−4 |
Check the result by substituting
−4 into the original equation.
|
y+9=5 |
Substitute −4 for y |
−4+9=?5 |
|
5=5 |
Since
y=−4 makes
y+9=5 a true statement, we found the solution to this equation.
example
Solve:
a−6=−8
Answer:
Solution
|
a−−6=−−8 |
Add 6 to each side to undo the subtraction. |
a−−6+6=−−8+6 |
Simplify. |
a=−−2 |
Check the result by substituting −2 into the original equation: |
a−−6=−−8 |
Substitute −2 for a |
−−2−−6=?−−8 |
|
−−8=−−8 |
The solution to
a−6=−8 is
−2.
Since
a=−2 makes
a−6=−8 a true statement, we found the solution to this equation.
example
Write an equation modeled by the envelopes and counters, and then solve it.

Solution
There are
4 envelopes, or
4 unknown values, on the left that match the
8 counters on the right. Let’s call the unknown quantity in the envelopes
x.
Write the equation. |
4x=8 |
Divide both sides by 4. |
44x |
Simplify. |
x=2 |
There are
2 counters in each envelope.
try it
Write the equation modeled by the envelopes and counters. Then solve it.
4x=12[/latex];[latex]x=3
Write the equation modeled by the envelopes and counters. Then solve it.
3x=6[/latex];[latex]x=2
example
Solve: 7x=−49.
Answer:
Solution
To isolate x, we need to undo multiplication.
|
7x=−−49 |
Divide each side by 7. |
77x=7−−49 |
Simplify. |
x=−−7 |
Check the solution.
|
7x=−49 |
Substitute −7 for x. |
7(−7)=?−49 |
|
−49=−49 |
Therefore,
−7 is the solution to the equation.
example
Solve:
−3y=63.
Answer:
Solution
To isolate y, we need to undo the multiplication.
|
−−3y=63 |
Divide each side by −3. |
−−3−−3y=−−363 |
Simplify |
y=−−21 |
Check the solution.
|
−3y=63 |
Substitute −21 for y. |
−3(−21)=?63 |
|
63=63 |
Since this is a true statement,
y=−21 is the solution to the equation.